Concept
Definition
Overview
A definition is a semantic statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.
In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what the mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where Definition is discussed.
This covert assertion is not a definition, but a postulate. The definition is a mere identical proposition, which gives information only about the use of language, and from which no conclusions affecting matters of fact can possibly be drawn. The accompanying postulate, on the other hand, affirms a fact, which may lead to consequences of every degree of importance.
John Stuart Mill, A System of Logic
names the idea; a chapter is titled for it; states what it is; author linked in the graph; opens on it
For the philosopher or the scientist it is a definition which applies to all the objects defined, and only those; it is the one satisfying the rules of logic. But in teaching it is not that; a good definition is one understood by the scholars. How does it happen that so many refuse to understand mathematics? Is that not something of a paradox? Lo and behold!
Henri Poincaré, The Foundations of Science
names the idea; a chapter is titled for it; states what it is; opens on it
In cases of this sort, though the definition is still a declaration of the meaning which in the particular instance the name is appointed to convey, it can not be said that to state the meaning of the word is the purpose of the definition. The purpose is not to expound a name, but a classification.
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
names the idea; states what it is; author linked in the graph; opens on it
In the second place, it may be admitted that the definition, like all definitions, is to a certain extent arbitrary. In the case of the small finite numbers, such as 2 and 3, it would be possible to frame definitions more nearly in accordance with our unanalysed feeling of what we mean; but the method of such definitions would lack uniformity, and would be found to fail sooner or later--at latest when we reached…
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
names the idea; states what it is; author linked in the graph; opens on it
Neglecting, then, the fundamental contradiction in this definition, the rest of our definitions follow without difficulty. The straight line is the relation between two points, and the plane is the relation between three.
Bertrand Russell, An essay on the foundations of geometry
names the idea; states what it is; author linked in the graph; opens on it
Philosophers who discussed Definition
- Philosophical Investigations
- Willard Van Orman Quine
- Blaise Pascal
- Robert Alexy
- Dionysius of Chalcedon
- António Castanheira Neves
Related ideas
- An Essay Concerning Human Understanding
- Word
- Imaginary number
- J. O. Urmson
- Neologism
- John Stuart Mill
- Analytic philosophy
- John Locke
- Posterior Analytics
- Necessity and sufficiency
- Ludwig Wittgenstein
- Mathematics
- Real number
- Natural language
- Natural number
- Philosophical Investigations
- Primitive notion
- J. L. Austin
- Peano axioms
- Recursion
- Set (mathematics)
- Subset
- Private language argument
- Self-reference
Place in the tradition
Part of Hundred Schools of Thought.